{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import sin\n",
    "\n",
    "xrand = np.random.normal(scale=4.,size=100)\n",
    "\n",
    "yrand = np.random.normal(scale=.5,size=100)\n",
    "yrand = [ (sin(xrand[i]) + yrand[i]) + 15 for i in range(len(xrand))]\n",
    "\n",
    "xrand *= 20.\n",
    "xrand += 1800.\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xrand, yrand, 'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lin(x,a,b):\n",
    "    return a*x + b\n",
    "\n",
    "ab,cov = curve_fit(lin,xrand,yrand,p0=(0,0))\n",
    "\n",
    "xfit = np.arange(min(xrand),max(xrand),20.)\n",
    "#yfit = [ab[0]*x+ab[1] for x in xfit]\n",
    "yfit = lin(xfit,*ab)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xrand, yrand, 'o', xfit, yfit)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt \n",
    "\n",
    "ab,cov = curve_fit(lin,xrand[::2],yrand[::2],p0=(0,0))\n",
    "\n",
    "def sqerr(x,y,f,par):\n",
    "    fit = f(x,*par)\n",
    "    diff = fit - y\n",
    "    return sqrt(np.sum(np.vectorize(lambda x: x*x)(diff))) / len(x)\n",
    "\n",
    "print(\"fit err: \",sqerr(xrand[::2],yrand[::2],lin,ab))\n",
    "print(\"test err: \",sqerr(xrand[1::2],yrand[1::2],lin,ab))    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sinscaled(xarr,a,b,c,d):\n",
    "    return np.array([a*sin(b*x+c)+d for x in xarr])\n",
    "\n",
    "abcd,cov = curve_fit(sinscaled,xrand,yrand,p0=[1.,.04,0.,15.])\n",
    "\n",
    "xfit = np.arange(min(xrand),max(xrand),2.)\n",
    "yfit = sinscaled(xfit,*abcd)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xrand, yrand, 'o', xfit, yfit)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "abcd,cov = curve_fit(sinscaled,xrand[::2],yrand[::2],p0=[1.,.04,0.,15.])\n",
    "\n",
    "print(\"fit err: \",sqerr(xrand[::2],yrand[::2],sinscaled,abcd))\n",
    "print(\"test err: \",sqerr(xrand[1::2],yrand[1::2],sinscaled,abcd))    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def doublesin(xarr,a,b,c,d,a2,b2,c2):\n",
    "    return np.array([a*sin(b*x+c)+d+a2*sin(b2*x+c2) for x in xarr])\n",
    "\n",
    "par,cov = curve_fit(doublesin,xrand,yrand,p0=[1.,.04,0.,15.,5.,.5,0.])\n",
    "\n",
    "xfit = np.arange(min(xrand),max(xrand),2.)\n",
    "yfit = doublesin(xfit,*par)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xrand, yrand, 'o', xfit, yfit)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "par,cov = curve_fit(doublesin,xrand[::2],yrand[::2],p0=[1.,.04,0.,15.,5.,.5,0.])\n",
    "\n",
    "print(\"fit err: \",sqerr(xrand[::2],yrand[::2],doublesin,par))\n",
    "print(\"test err: \",sqerr(xrand[1::2],yrand[1::2],doublesin,par))    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly(xarr,*par):\n",
    "    val = np.zeros(len(xarr))\n",
    "    for i in range(len(xarr)):\n",
    "        xp = 1\n",
    "        for p in par:\n",
    "            val[i] += xp*p\n",
    "            xp *= xarr[i]\n",
    "    return val\n",
    "\n",
    "par,cov = curve_fit(poly,xrand,yrand,p0 = [15.] + [1.] * 8)\n",
    "\n",
    "xfit = np.arange(min(xrand),max(xrand),2.)\n",
    "yfit = poly(xfit,*par)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xrand, yrand, 'o', xfit, yfit)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "par,cov = curve_fit(poly,xrand[::2],yrand[::2],p0=[15.] + [1.] * 8)\n",
    "\n",
    "print(\"fit err: \",sqerr(xrand[::2],yrand[::2],poly,par))\n",
    "print(\"test err: \",sqerr(xrand[1::2],yrand[1::2],poly,par))    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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